Stat Computing > SAS > Textbook Examples > Multilevel Analysis, by Snijders and Bosker

SAS Textbook Examples
Multilevel Analysis by Tom Snijders and Roel Bosker
Chapter 4: The Random Intercept Model

In this chapter we create and use the variables GndC_verb which is equal to iq_verb centered around the grand mean; GrpMC_verb which contains the group means of GndC_verb, so it contains the group means of iq_verb centered around the grand mean.

Table 4.1, p. 47.
The random intercept only model.

proc mixed data=schools covtest noclprint noitprint method=ml;
  class schoolnr;
  model langpost = / solution;
  random intercept / subject=schoolnr;
run;

<output omitted>

                   Covariance Parameter Estimates

                                      Standard         Z
Cov Parm      Subject     Estimate       Error     Value        Pr Z
Intercept     schoolNR     19.4126      3.0962      6.27      <.0001
Residual                   64.5704      1.9729     32.73      <.0001


           Fit Statistics
-2 Log Likelihood             16253.2
AIC (smaller is better)       16259.2
AICC (smaller is better)      16259.2
BIC (smaller is better)       16267.8

                   Solution for Fixed Effects

                         Standard
Effect       Estimate       Error      DF    t Value    Pr > |t|
Intercept     40.3642      0.4262     130      94.70      <.0001

Creating the variable GndC_verb which is equal to iq_verb centered around the grand mean.

proc sql;
  create table schools1 as
  select *, iq_verb - mean(iq_verb) as GndC_verb
  from schools;
quit;

Table 4.2, p. 49.
Random intercept model with effect for IQ centered around the grand mean.

proc mixed data=schools1 covtest noclprint noitprint;
  class schoolnr;
  model langpost = GndC_verb / solution;
  random intercept / subject=schoolnr;
run;

<output omitted>

                   Covariance Parameter Estimates
                   
                                      Standard         Z
Cov Parm      Subject     Estimate       Error     Value        Pr Z
Intercept     schoolNR      9.6015      1.5927      6.03      <.0001
Residual                   42.2446      1.2893     32.77      <.0001


           Fit Statistics
-2 Res Log Likelihood         15255.8
AIC (smaller is better)       15259.8
AICC (smaller is better)      15259.8
BIC (smaller is better)       15265.5

                   Solution for Fixed Effects

                         Standard
Effect       Estimate       Error      DF    t Value    Pr > |t|
Intercept     40.6082      0.3082     130     131.77      <.0001
GndC_verb      2.4876     0.07008    2155      35.50      <.0001

Fig. 4.2, p. 49.
Randomly chosen regression lines according to the random intercept model of table 4.4.

proc mixed data=schools2 covtest noitprint noclprint method=ml;
class schoolnr;
model langpost = GndC_verb / outp=p ;
random intercept / subject=schoolnr type=un;
run;
goptions reset=all;
symbol i=j r=24;
axis1 order=(-4 to 4 by 1) label=('IQ');
axis2 order=(20 to 60 by 5) label=(a=90 'Predicted');
proc gplot data=p;
where schoolnr < 27;
plot pred*GndC_verb = schoolnr / vaxis=axis2 haxis=axis1 href=0 ;
run;
quit;

Table 4.3, p. 51.
Ordinary least squares regression of the model in table 4.2.

proc reg data=schools1;
  model langpost = GndC_verb;
run;
quit;
                             Analysis of Variance

                                    Sum of           Mean
Source                   DF        Squares         Square    F Value    Pr > F
Model                     1          68916          68916    1352.84    <.0001
Error                  2285         116402       50.94159
Corrected Total        2286         185317

Root MSE              7.13734    R-Square     0.3719
Dependent Mean       40.93485    Adj R-Sq     0.3716
Coeff Var            17.43585

                        Parameter Estimates

                     Parameter       Standard
Variable     DF       Estimate          Error    t Value    Pr > |t|
Intercept     1       40.93485        0.14925     274.28      <.0001
GndC_verb     1        2.65390        0.07215      36.78      <.0001

Table 4.4, p. 55.
Random intercept model with different within and between group regressions.
Note: The "IQ here is the raw variable" means that we are using the grand mean centered variable GndC_verb and not iq_verb. Furthermore, the group mean variable for IQ is actually the group mean variable of GndC_verb which we here have called GrpMC_verb.

*Group mean centering of GndC_verb. ;
proc sql;
  create table schools2 as
  select *, mean(GndC_verb) as GrpMC_verb
  from schools1
  group by schoolnr;
quit;
proc mixed data=schools2 covtest noitprint noclprint method=ml;
  class schoolnr;
  model langpost = GndC_verb GrpMC_verb / solution;
  random intercept / subject=schoolnr;
run; 

<output omitted>
                   Covariance Parameter Estimates

                                      Standard         Z
Cov Parm      Subject     Estimate       Error     Value        Pr Z
Intercept     schoolNR      7.7275      1.3093      5.90      <.0001
Residual                   42.1519      1.2842     32.82      <.0001


           Fit Statistics

-2 Log Likelihood             15227.5
AIC (smaller is better)       15237.5
AICC (smaller is better)      15237.6
BIC (smaller is better)       15251.9


                   Solution for Fixed Effects

                          Standard
Effect        Estimate       Error      DF    t Value    Pr > |t|
Intercept      40.7423      0.2844     129     143.26      <.0001
GndC_verb       2.4148     0.07166    2155      33.70      <.0001
GrpMC_verb      1.5885      0.3127    2155       5.08      <.0001

The remaining tables and figures have been skipped.

UCLA Researchers are invited to our Statistical Consulting Services
We recommend others to our list of Other Resources for Statistical Computing Help
These pages are Copyrighted (c) by UCLA Academic Technology Services